Embedded interaction code recognition

ABSTRACT

In accordance with embodiments of the invention, embedded interaction code (EIC) symbols are recognized. EIC dots are generated based on effective EIC symbols, which have been generated by processing an image containing the EIC symbols, by obtaining graylevels of selected positions of the EIC-symbols. Rotated EIC dots are generated based on the EIC dots by determining which grid cells correspond to the EIC symbols and by determining which direction is a correct orientation of the EIC symbols. A homography matrix is updated with orientation information based on the EIC dots. EIC bits are extracted from the rotated EIC dots based on graylevels of selected positions of the rotated EIC dots.

TECHNICAL FIELD

Embodiments of the invention relate to image processing and moreparticularly relate to embedded interaction code recognition.

BACKGROUND

Computer users are accustomed to using a mouse and keyboard as a way ofinteracting with a personal computer. While personal computers provide anumber of advantages over written documents, most users continue toperform certain functions using printed paper. Some of these functionsinclude reading and annotating written documents. In the case ofannotations, the printed document assumes a greater significance becauseof the annotations made on it by the user. One of the difficulties,however, with having a printed document with annotations is the need tohave the annotations subsequently entered back into the electronic formof the document. This requires the original user or another user to wadethrough the annotations and enter them into a personal computer. In somecases, a user will scan in the annotations and the original text,thereby creating a new document. These multiple steps make theinteraction between the printed document and the electronic version ofthe document difficult to handle on a repeated basis. Further,scanned-in images are frequently non-modifiable. There may be no way toseparate the annotations from the original text. This makes using theannotations difficult. Accordingly, an improved way of handlingannotations would be desirable.

One technique for capturing handwritten information is by using an imagecapturing pen whose location may be determined during writing. One imagecapturing pen that provides this capability is the Anoto pen by AnotoInc. This pen functions by using a camera to capture an image of paperencoded with a predefined pattern. An example of the image pattern isshown in FIG. 11. This pattern is used by the Anoto pen to determine alocation of the pen on a piece of paper (or other positionally encodedmedium).

Improved techniques for recognizing embedded interaction code (EIC)information, based on images of EIC documents, would be desirable.

SUMMARY

In accordance with embodiments of the invention, embedded interactioncode (EIC) symbols are recognized. EIC dots are generated based oneffective EIC symbols, which have been generated by processing an imagecontaining the EIC symbols, by obtaining graylevels of selectedpositions of the EIC-symbols. Rotated EIC dots are generated based onthe EIC dots by determining which grid cells correspond to the EICsymbols and by determining which direction is a correct orientation ofthe EIC symbols. A homography matrix is updated with orientationinformation based on the EIC dots. EIC bits are extracted from therotated EIC dots based on graylevels of selected positions of therotated EIC dots

These and other aspects of the present invention will become knownthrough the following drawings and associated description.

BRIEF DESCRIPTION OF DRAWINGS

The foregoing summary of the invention, as well as the followingdetailed description of preferred embodiments, is better understood whenread in conjunction with the accompanying drawings, which are includedby way of example, and not by way of limitation with regard to theclaimed invention.

FIG. 1 shows a general description of a computer that may be used inconjunction with embodiments of the present invention.

FIGS. 2A and 2B show an image capture system and corresponding capturedimage in accordance with embodiments of the present invention.

FIGS. 3A through 3F show various sequences and folding techniques inaccordance with embodiments of the present invention.

FIGS. 4A through 4E show various encoding systems in accordance withembodiments of the present invention.

FIGS. 5A through 5D show four possible resultant corners associated withthe encoding system according to FIGS. 4A and 4B.

FIG. 6 shows rotation of a captured image portion in accordance withembodiments of the present invention.

FIG. 7 shows various angles of rotation used in conjunction with thecoding system of FIGS. 4A through 4E.

FIG. 8 shows a process for determining the location of a captured arrayin accordance with embodiments of the present invention.

FIG. 9 shows a method for determining the location of a captured imagein accordance with embodiments of the present invention.

FIG. 10 shows another method for determining the location of capturedimage in accordance with embodiments of the present invention.

FIG. 11 shows a representation of encoding space in a document accordingto prior art.

FIG. 12 shows a flow diagram for decoding extracted bits from a capturedimage in accordance with embodiments of the present invention.

FIG. 13 shows an example of a camera captured image of an EIC documentin accordance with embodiments of the invention.

FIG. 14 shows symbol, grid, and image coordinate systems in accordancewith embodiments of the invention.

FIG. 15 shows symbol, grid, and image coordinate systems of a differentimage than the image shown in FIG. 14 in accordance with embodiments ofthe invention.

FIG. 16 shows a flow diagram of a system for performing EIC symbolrecognition in accordance with embodiments of the invention.

FIG. 17 shows effective EIC symbols in accordance with embodiments ofthe invention.

FIG. 18 shows EIC bits in accordance with embodiments of the invention.

FIG. 19 shows a shifted coordinate system in which grid intersections inan image have non-negative coordinates in accordance with embodiments ofthe invention.

FIG. 20 shows positions on each edge of an EIC symbol in accordance withembodiments of the invention.

FIG. 21 shows an example of an EIC symbol in accordance with embodimentsof the invention.

FIG. 22 shows a pixel index in accordance with embodiments of theinvention.

FIG. 23 shows pixels for bilinear sampling in accordance withembodiments of the invention.

FIG. 24 shows position naming on each edge in accordance withembodiments of the invention.

FIG. 25 shows grid cells and various symbol orientations in accordancewith embodiments of the invention.

FIG. 26 shows EIC symbol rotation in accordance with embodiments of theinvention.

FIG. 27 shows EIC symbol offset in accordance with embodiments of theinvention.

FIG. 28 shows coordinate systems of symbol, grid, and image when Q=0 inaccordance with embodiments of the invention.

FIG. 29 shows coordinate systems of symbol, grid, and image when Q=1 inaccordance with embodiments of the invention.

FIG. 30 shows coordinate systems of symbol, grid, and image when Q=2 inaccordance with embodiments of the invention.

FIG. 31 shows coordinate systems of symbol, grid, and image when Q=3 inaccordance with embodiments of the invention.

FIG. 32 shows assignment of bit values in accordance with embodiments ofthe invention.

DETAILED DESCRIPTION

Aspects of the present invention relate to determining the location of acaptured image in relation to a larger image. The location determinationmethod and system described herein may be used in combination with amulti-function pen.

The following is separated by subheadings for the benefit of the reader.The subheadings include: terms, general-purpose computer, imagecapturing pen, encoding of array, decoding, error correction, locationdetermination, and embedded interaction code recognition.

Terms

Pen—any writing implement that may or may not include the ability tostore ink. In some examples, a stylus with no ink capability may be usedas a pen in accordance with embodiments of the present invention.

Camera—an image capture system that captures an image from paper or anyother medium.

General Purpose Computer

FIG. 1 is a functional block diagram of an example of a conventionalgeneral-purpose digital computing environment that can be used toimplement various aspects of the present invention. In FIG. 1, acomputer 100 includes a processing unit 110, a system memory 120, and asystem bus 130 that couples various system components including thesystem memory to the processing unit 110. The system bus 130 may be anyof several types of bus structures including a memory bus or memorycontroller, a peripheral bus, and a local bus using any of a variety ofbus architectures. The system memory 120 includes read only memory (ROM)140 and random access memory (RAM) 150.

A basic input/output system 160 (BIOS), containing the basic routinesthat help to transfer information between elements within the computer100, such as during start-up, is stored in the ROM 140. The computer 100also includes a hard disk drive 170 for reading from and writing to ahard disk (not shown), a magnetic disk drive 180 for reading from orwriting to a removable magnetic disk 190, and an optical disk drive 191for reading from or writing to a removable optical disk 192 such as a CDROM or other optical media. The hard disk drive 170, magnetic disk drive180, and optical disk drive 191 are connected to the system bus 130 by ahard disk drive interface 192, a magnetic disk drive interface 193, andan optical disk drive interface 194, respectively. The drives and theirassociated computer-readable media provide nonvolatile storage ofcomputer readable instructions, data structures, program modules andother data for the personal computer 100. It will be appreciated bythose skilled in the art that other types of computer readable mediathat can store data that is accessible by a computer, such as magneticcassettes, flash memory cards, digital video disks, Bernoullicartridges, random access memories (RAMs), read only memories (ROMs),and the like, may also be used in the example operating environment.

A number of program modules can be stored on the hard disk drive 170,magnetic disk 190, optical disk 192, ROM 140 or RAM 150, including anoperating system 195, one or more application programs 196, otherprogram modules 197, and program data 198. A user can enter commands andinformation into the computer 100 through input devices such as akeyboard 101 and pointing device 102. Other input devices (not shown)may include a microphone, joystick, game pad, satellite dish, scanner orthe like. These and other input devices are often connected to theprocessing unit 110 through a serial port interface 106 that is coupledto the system bus, but may be connected by other interfaces, such as aparallel port, game port or a universal serial bus (USB). Further still,these devices may be coupled directly to the system bus 130 via anappropriate interface (not shown). A monitor 107 or other type ofdisplay device is also connected to the system bus 130 via an interface,such as a video adapter 108. In addition to the monitor, personalcomputers typically include other peripheral output devices (not shown),such as speakers and printers. In a preferred embodiment, a pendigitizer 165 and accompanying pen or stylus 166 are provided in orderto digitally capture freehand input. Although a direct connectionbetween the pen digitizer 165 and the serial port is shown, in practice,the pen digitizer 165 may be coupled to the processing unit 110directly, via a parallel port or other interface and the system bus 130as known in the art. Furthermore, although the digitizer 165 is shownapart from the monitor 107, it is preferred that the usable input areaof the digitizer 165 be co-extensive with the display area of themonitor 107. Further still, the digitizer 165 may be integrated in themonitor 107, or may exist as a separate device overlaying or otherwiseappended to the monitor 107.

The computer 100 can operate in a networked environment using logicalconnections to one or more remote computers, such as a remote computer109. The remote computer 109 can be a server, a router, a network PC, apeer device or other common network node, and typically includes many orall of the elements described above relative to the computer 100,although only a memory storage device 111 has been illustrated inFIG. 1. The logical connections depicted in FIG. 1 include a local areanetwork (LAN) 112 and a wide area network (WAN) 113. Such networkingenvironments are commonplace in offices, enterprise-wide computernetworks, intranets and the Internet.

When used in a LAN networking environment, the computer 100 is connectedto the local network 112 through a network interface or adapter 114.When used in a WAN networking environment, the personal computer 100typically includes a modem 115 or other means for establishing acommunications over the wide area network 113, such as the Internet. Themodem 115, which may be internal or external, is connected to the systembus 130 via the serial port interface 106. In a networked environment,program modules depicted relative to the personal computer 100, orportions thereof, may be stored in the remote memory storage device.

It will be appreciated that the network connections shown areillustrative and other techniques for establishing a communications linkbetween the computers can be used. The existence of any of variouswell-known protocols such as TCP/IP, Ethernet, FTP, HTTP, Bluetooth,IEEE 802.11x and the like is presumed, and the system can be operated ina client-server configuration to permit a user to retrieve web pagesfrom a web-based server. Any of various conventional web browsers can beused to display and manipulate data on web pages.

Image Capturing Pen

Aspects of the present invention include placing an encoded data streamin a displayed form that represents the encoded data stream. (Forexample, as will be discussed with FIG. 4B, the encoded data stream isused to create a graphical pattern.) The displayed form may be printedpaper (or other physical medium) or may be a display projecting theencoded data stream in conjunction with another image or set of images.For example, the encoded data stream may be represented as a physicalgraphical image on the paper or a graphical image overlying thedisplayed image (e.g., representing the text of a document) or may be aphysical (non-modifiable) graphical image on a display screen (so anyimage portion captured by a pen is locatable on the display screen).

This determination of the location of a captured image may be used todetermine the location of a user's interaction with the paper, medium,or display screen. In some aspects of the present invention, the pen maybe an ink pen writing on paper. In other aspects, the pen may be astylus with the user writing on the surface of a computer display. Anyinteraction may be provided back to the system with knowledge of theencoded image on the document or supporting the document displayed onthe computer screen. By repeatedly capturing images with a camera in thepen or stylus as the pen or stylus traverses a document, the system cantrack movement of the stylus being controlled by the user. The displayedor printed image may be a watermark associated with the blank orcontent-rich paper or may be a watermark associated with a displayedimage or a fixed coding overlying a screen or built into a screen.

FIGS. 2A and 2B show an illustrative example of pen 201 with a camera203. Pen 201 includes a tip 202 that may or may not include an inkreservoir. Camera 203 captures an image 204 from surface 207. Pen 201may further include additional sensors and/or processors as representedin broken box 206. These sensors and/or processors 206 may also includethe ability to transmit information to another pen 201 and/or a personalcomputer (for example, via Bluetooth or other wireless protocols).

FIG. 2B represents an image as viewed by camera 203. In one illustrativeexample, the field of view of camera 203 (i.e., the resolution of theimage sensor of the camera) is 32×32 pixels (where N=32). In theembodiment, a captured image (32 pixels by 32 pixels) corresponds to anarea of approximately 5 mm by 5 mm of the surface plane captured bycamera 203. Accordingly, FIG. 2B shows a field of view of 32 pixels longby 32 pixels wide. The size of N is adjustable, such that a larger Ncorresponds to a higher image resolution. Also, while the field of viewof the camera 203 is shown as a square for illustrative purposes here,the field of view may include other shapes as is known in the art.

The images captured by camera 203 may be defined as a sequence of imageframes {I_(i)}, where I_(i) is captured by the pen 201 at sampling timet_(i). The sampling rate may be large or small, depending on systemconfiguration and performance requirement. The size of the capturedimage frame may be large or small, depending on system configuration andperformance requirement.

The image captured by camera 203 may be used directly by the processingsystem or may undergo pre-filtering. This pre-filtering may occur in pen201 or may occur outside of pen 201 (for example, in a personalcomputer).

The image size of FIG. 2B is 32×32 pixels. If each encoding unit size is3×3 pixels, then the number of captured encoded units would beapproximately 100 units. If the encoding unit size is 5×5 pixels, thenthe number of captured encoded units is approximately 36.

FIG. 2A also shows the image plane 209 on which an image 210 of thepattern from location 204 is formed. Light received from the pattern onthe object plane 207 is focused by lens 208. Lens 208 may be a singlelens or a multi-part lens system, but is represented here as a singlelens for simplicity. Image capturing sensor 211 captures the image 210.

The image sensor 211 may be large enough to capture the image 210.Alternatively, the image sensor 211 may be large enough to capture animage of the pen tip 202 at location 212. For reference, the image atlocation 212 is referred to as the virtual pen tip. It is noted that thevirtual pen tip location with respect to image sensor 211 is fixedbecause of the constant relationship between the pen tip, the lens 208,and the image sensor 211.

The following transformation F_(S→P) transforms position coordinates inthe image captured by camera to position coordinates in the real imageon the paper:L _(paper) =F _(SΔP)(L _(Sensor)).

During writing, the pen tip and the paper are on the same plane.Accordingly, the transformation from the virtual pen tip to the real pentip is also F_(S→P):L _(pentip) =F _(S→P)(L _(virtual-pentip)).

The transformation F_(S→P) may be estimated as an affine transform,which approximates F_(S→P) as: ${F_{S->P}^{\prime} = \begin{bmatrix}\frac{\sin\quad\theta_{y}}{s_{x}} & \frac{\cos\quad\theta_{y}}{s_{x}} & 0 \\\frac{{- \sin}\quad\theta_{x}}{s_{y}} & \frac{{- \cos}\quad\theta_{x}}{s_{y}} & 0 \\0 & 0 & 1\end{bmatrix}},$in which θ_(x), θ_(y), s_(x), and s_(y) are the rotation and scale oftwo orientations of the pattern captured at location 204. Further, onecan refine F′_(S→P) by matching the captured image with thecorresponding real image on paper. “Refine” means to get a more preciseestimation of the transformation F_(S→P) by a type of optimizationalgorithm referred to as a recursive method. The recursive method treatsthe matrix F′_(S→P) as the initial value. The refined estimationdescribes the transformation between S and P more precisely.

Next, one can determine the location of virtual pen tip by calibration.

One places the pen tip 202 on a fixed location L_(pentip) on paper.Next, one tilts the pen, allowing the camera 203 to capture a series ofimages with different pen poses. For each image captured, one may obtainthe transformation F_(S→P). From this transformation, one can obtain thelocation of the virtual pen tip L_(virtual-pentip):L _(virtual-pentip) =F _(S→P)(L _(pentip)),where L_(pentip) is initialized as (0, 0) andF_(S→P)=(F_(S→P))⁻¹.

By averaging the L_(virtual-pentip) obtained from each image, a locationof the virtual pen tip L_(virtual-pentip) may be determined. WithL_(virtual-pentip), one can get a more accurate estimation ofL_(pentip). After several times of iteration, an accurate location ofvirtual pen tip L_(virtual-pentip) may be determined.

The location of the virtual pen tip L_(virtual-pentip) is now known. Onecan also obtain the transformation F_(S→P) from the images captured.Finally, one can use this information to determine the location of thereal pen tip L_(pentip):L _(pentip) =F _(S→P)(L _(virtual-pentip)).Encoding of Array

A two-dimensional array may be constructed by folding a one-dimensionalsequence. Any portion of the two-dimensional array containing a largeenough number of bits may be used to determine its location in thecomplete two-dimensional array. However, it may be necessary todetermine the location from a captured image or a few captured images.So as to minimize the possibility of a captured image portion beingassociated with two or more locations in the two-dimensional array, anon-repeating sequence may be used to create the array. One property ofa created sequence is that the sequence does not repeat over aparticular length (or window size). The following describes the creationof the one-dimensional sequence then the folding of the sequence into anarray.

Sequence Construction

A sequence of numbers may be used as the starting point of the encodingsystem. For example, a sequence (also referred to as an m-sequence) maybe represented as a q-element set in field F_(q). Here, q=p^(n), wheren≧1 and p is a prime number. The sequence or m-sequence may be generatedby a variety of different techniques including, but not limited to,polynomial division. Using polynomial division, the sequence may bedefined as follows: $\frac{R_{l}(x)}{P_{n}(x)},$

where P_(n)(x) is a primitive polynomial of degree n in field F_(q)[x](having q^(n) elements). R_(l)(x) is a nonzero polynomial of degree l(where l<n) in field F_(q)[x]. The sequence may be created using aniterative procedure with two steps: first, dividing the two polynomials(resulting in an element of field F_(q)) and, second, multiplying theremainder by x. The computation stops when the output begins to repeat.This process may be implemented using a linear feedback shift registeras set forth in an article by Douglas W. Clark and Lih-Jyh Weng,“Maximal and Near-Maximal Shift Register Sequences: Efficient EventCounters and Easy Discrete Logarithms,” IEEE Transactions on Computers43.5 (May 1994, pp 560-568). In this environment, a relationship isestablished between cyclical shifting of the sequence and polynomialR_(l)(x): changing R_(l)(x) only cyclically shifts the sequence andevery cyclical shifting corresponds to a polynomial R_(l)(x). One of theproperties of the resulting sequence is that, the sequence has a periodof q^(n)−1 and within a period, over a width (or length) n, any portionexists once and only once in the sequence. This is called the “windowproperty”. Period q^(n)−1 is also referred to as the length of thesequence and n as the order of the sequence. In our implementation, q ischosen as 2.

The process described above is but one of a variety of processes thatmay be used to create a sequence with the window property.

Array Construction

The array (or m-array) that may be used to create the image (of which aportion may be captured by the camera) is an extension of theone-dimensional sequence or m-sequence. Let A be an array of period (m₁,m₂), namely A(k+m₁,l)=A(k,l+m₂)=A(k,l). When an n₁×n₂ window shiftsthrough a period of A, all the nonzero n₁×n₂ matrices over F_(q) appearonce and only once. This property is also referred to as a “windowproperty” in that each window is unique. A widow may then be expressedas an array of period (m₁, m₂) (with m₁ and m₂ being the horizontal andvertical number of bits present in the array) and order (n₁, n₂).

A binary array (or m-array) may be constructed by folding the sequence.One approach is to obtain a sequence then fold it to a size of m₁×m₂where the length of the array is L=m₁×m₂=2^(n)−1. Alternatively, one maystart with a predetermined size of the space that one wants to cover(for example, one sheet of paper, 30 sheets of paper or the size of acomputer monitor), determine the area (m₁×m₂), then use the size to letL≧m₁×m₂, where L=2^(n)−1.

A variety of different folding techniques may be used. For example,FIGS. 3A through 3C show three different sequences. Each of these may befolded into the array shown as FIG. 3D. The three different foldingmethods are shown as the overlay in FIG. 3D and as the raster paths inFIGS. 3E and 3F. We adopt the folding method shown in FIG. 3D.

To create the folding method as shown in FIG. 3D, one creates a sequence{a_(i)} of length L and order n. Next, an array {b_(kl)} of size m₁×m₂,where gcd(m₁, m₂)=1 and L=m₁×m₂, is created from the sequence {a_(i)} byletting each bit of the array be calculated as shown by equation 1:b_(kl)=a_(i), where k=i mod(m₁), l=i mod(m₂), i=0, . . . ,L−1.  (1)

This folding approach may be alternatively expressed as laying thesequence on the diagonal of the array, then continuing from the oppositeedge when an edge is reached.

FIG. 4A shows sample encoding techniques that may be used to encode thearray of FIG. 3D. It is appreciated that other encoding techniques maybe used. For example, an alternative coding technique is shown in FIG.11.

Referring to FIG. 4A, a first bit 401 (for example, “1”) is representedby a column of dark ink. A second bit 402 (for example, “0”) isrepresented by a row of dark ink. It is appreciated that any color inkmay be used to represent the various bits. The only requirement in thecolor of the ink chosen is that it provides a significant contrast withthe background of the medium to be differentiable by an image capturesystem. The bits in FIG. 4A are represented by a 3×3 matrix of cells.The size of the matrix may be modified to be any size as based on thesize and resolution of an image capture system. Alternativerepresentation of bits 0 and 1 are shown in FIGS. 4C-4E. It isappreciated that the representation of a one or a zero for the sampleencodings of FIGS. 4A-4E may be switched without effect. FIG. 4C showsbit representations occupying two rows or columns in an interleavedarrangement. FIG. 4D shows an alternative arrangement of the pixels inrows and columns in a dashed form. Finally FIG. 4E shows pixelrepresentations in columns and rows in an irregular spacing format(e.g., two dark dots followed by a blank dot).

Referring back to FIG. 4A, if a bit is represented by a 3×3 matrix andan imaging system detects a dark row and two white rows in the 3×3region, then a zero is detected (or one). If an image is detected with adark column and two white columns, then a one is detected (or a zero).

Here, more than one pixel or dot is used to represent a bit. Using asingle pixel (or bit) to represent a bit is fragile. Dust, creases inpaper, non-planar surfaces, and the like create difficulties in readingsingle bit representations of data units. However, it is appreciatedthat different approaches may be used to graphically represent the arrayon a surface. Some approaches are shown in FIGS. 4C through 4E. It isappreciated that other approaches may be used as well. One approach isset forth in FIG. 11 using only space-shifted dots.

A bit stream is used to create the graphical pattern 403 of FIG. 4B.Graphical pattern 403 includes 12 rows and 18 columns. The rows andcolumns are formed by a bit stream that is converted into a graphicalrepresentation using bit representations 401 and 402. FIG. 4B may beviewed as having the following bit representation: $\begin{bmatrix}0 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \\1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 \\1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0\end{bmatrix}\quad$Decoding

When a person writes with the pen of FIG. 2A or moves the pen close tothe encoded pattern, the camera captures an image. For example, pen 201may utilize a pressure sensor as pen 201 is pressed against paper andpen 201 traverses a document on the paper. The image is then processedto determine the orientation of the captured image with respect to thecomplete representation of the encoded image and extract the bits thatmake up the captured image.

For the determination of the orientation of the captured image relativeto the whole encoded area, one may notice that not all the fourconceivable corners shown in FIG. 5A-5D can present in the graphicalpattern 403. In fact, with the correct orientation, the type of cornershown in FIG. 5A cannot exist in the graphical pattern 403. Therefore,the orientation in which the type of corner shown in FIG. 5A is missingis the right orientation.

Continuing to FIG. 6, the image captured by a camera 601 may be analyzedand its orientation determined so as to be interpretable as to theposition actually represented by the image 601. First, image 601 isreviewed to determine the angle θ needed to rotate the image so that thepixels are horizontally and vertically aligned. It is noted thatalternative grid alignments are possible including a rotation of theunderlying grid to a non-horizontal and vertical arrangement (forexample, 45 degrees). Using a non-horizontal and vertical arrangementmay provide the probable benefit of eliminating visual distractions fromthe user, as users may tend to notice horizontal and vertical patternsbefore others. For purposes of simplicity, the orientation of the grid(horizontal and vertical and any other rotation of the underlying grid)is referred to collectively as the predefined grid orientation.

Next, image 601 is analyzed to determine which corner is missing. Therotation amount o needed to rotate image 601 to an image ready fordecoding 603 is shown as o=(θ plus a rotation amount {defined by whichcorner missing}). The rotation amount is shown by the equation in FIG.7. Referring back to FIG. 6, angle θ is first determined by the layoutof the pixels to arrive at a horizontal and vertical (or otherpredefined grid orientation) arrangement of the pixels and the image isrotated as shown in 602. An analysis is then conducted to determine themissing corner and the image 602 rotated to the image 603 to set up theimage for decoding. Here, the image is rotated 90 degreescounterclockwise so that image 603 has the correct orientation and canbe used for decoding.

It is appreciated that the rotation angle θ may be applied before orafter rotation of the image 601 to account for the missing corner. It isalso appreciated that by considering noise in the captured image, allfour types of corners may be present. We may count the number of cornersof each type and choose the type that has the least number as the cornertype that is missing.

Finally, the code in image 603 is read out and correlated with theoriginal bit stream used to create image 403. The correlation may beperformed in a number of ways. For example, it may be performed by arecursive approach in which a recovered bit stream is compared againstall other bit stream fragments within the original bit stream. Second, astatistical analysis may be performed between the recovered bit streamand the original bit stream, for example, by using a Hamming distancebetween the two bit streams. It is appreciated that a variety ofapproaches may be used to determine the location of the recovered bitstream within the original bit stream.

As will be discussed, EIC pattern analysis obtains recovered bits fromimage 603. Once one has the recovered bits, one needs to locate thecaptured image within the original array (for example, the one shown inFIG. 4B). The process of determining the location of a segment of bitswithin the entire array is complicated by a number of items. First, theactual bits to be captured may be obscured (for example, the camera maycapture an image with handwriting that obscures the original code).Second, dust, creases, reflections, and the like may also create errorsin the captured image. These errors make the localization process moredifficult. In this regard, the image capture system may need to functionwith non-sequential bits extracted from the image. The followingrepresents a method for operating with non-sequential bits from theimage.

Let the sequence (or m-sequence) I correspond to the power seriesI(x)=1/P_(n)(x), where n is the order of the m-sequence, and thecaptured image contains K bits of I b=(b₀ b₁ b₂ . . . b_(K-1))^(t),where K≧n and the superscript t represents a transpose of the matrix orvector. The location s of the K bits is just the number of cyclic shiftsof I so that b₀ is shifted to the beginning of the sequence. Then thisshifted sequence R corresponds to the power series x^(s)/P_(n)(x), orR=T^(s) (I), where T is the cyclic shift operator. We find this sindirectly. The polynomials modulo P_(n)(x) form a field. It isguaranteed that x^(s)≡r₀+r₁x+ . . . r_(n-1)x^(n−1)mod(P_(n)(x)).Therefore, we may find (r₀,r₁, . . . ,r_(n-1)) and then solve for s.

The relationship x^(s)≡r₀+r₁x+ . . . r_(n-1)x^(n−1)mod(P_(n)(x)) impliesthat R=r₀+r₁T(I)+ . . . +r_(n-1)T^(n−1)(I). Written in a binary linearequation, it becomes:R=r^(t)A  (2)where r=(r₀ r₁ r₂ . . . r_(n-1))^(t), and A=(I T(I) . . . T^(n−1)(I)^(t)which consists of the cyclic shifts of I from 0-shift to (n−1)-shift.Now only sparse K bits are available in R to solve r. Let the indexdifferences between b_(i) and b₀ in R be k_(i), i=1,2, . . . , k−1, thenthe 1^(st) and (k_(i)+1)-th elements of R, i=1,2, . . . ,k−1, areexactly b₀, b₁, . . . , b_(k−1). By selecting the 1^(st) and(k_(i)+1)-th columns of A, i=1,2, . . . ,k−1, the following binarylinear equation is formed:b^(t)=r^(t)M  (3)

where M is an n×K sub-matrix of A.

If b is error-free, the solution of r may be expressed as:r^(t)={tilde over (b)}^(t){tilde over (M)}⁻¹  (4)

where {tilde over (M)} is any non-degenerate n×n sub-matrix of M and{tilde over (b)} is the corresponding sub-vector of b.

With known r, we may use the Pohlig-Hellman-Silver algorithm as noted byDouglas W. Clark and Lih-Jyh Weng, “Maximal and Near-Maximal ShiftRegister Sequences: Efficient Event Counters and Easy DiscreteLogorithms,” IEEE Transactions on Computers 43.5 (May 1994, pp 560-568)to find s so that x^(s)≡r₀+r₁x+ . . . r_(n-1)x^(n−1)mod(P_(n)(x)).

As matrix A (with the size of n by L, where L=2^(n)−1) may be huge, weshould avoid storing the entire matrix A. In fact, as we have seen inthe above process, given extracted bits with index difference k_(i),only the first and (k_(i)+1)-th columns of A are relevant to thecomputation. Such choices of k_(i) is quite limited, given the size ofthe captured image. Thus, only those columns that may be involved incomputation need to saved. The total number of such columns is muchsmaller than L (where L=2^(n)−1 is the length of the m-sequence).

Error Correction

If errors exist in b, then the solution of r becomes more complex.Traditional methods of decoding with error correction may not readilyapply, because the matrix M associated with the captured bits may changefrom one captured image to another.

We adopt a stochastic approach. Assuming that the number of error bitsin b, n_(e), is relatively small compared to K, then the probability ofchoosing correct n bits from the K bits of b and the correspondingsub-matrix {tilde over (M)} of M being non-degenerate is high.

When the n bits chosen are all correct, the Hamming distance betweenb^(t) and r^(t)M, or the number of error bits associated with r, shouldbe minimal, where r is computed via equation (4). Repeating the processfor several times, it is likely that the correct r that results in theminimal error bits can be identified.

If there is only one r that is associated with the minimum number oferror bits, then it is regarded as the correct solution. Otherwise, ifthere is more than one r that is associated with the minimum number oferror bits, the probability that n_(e) exceeds the error correctingability of the code generated by M is high and the decoding processfails. The system then may move on to process the next captured image.In another implementation, information about previous locations of thepen can be taken into consideration. That is, for each captured image, adestination area where the pen may be expected next can be identified.For example, if the user has not lifted the pen between two imagecaptures by the camera, the location of the pen as determined by thesecond image capture should not be too far away from the first location.Each r that is associated with the minimum number of error bits can thenbe checked to see if the location s computed from r satisfies the localconstraint, i.e., whether the location is within the destination areaspecified.

If the location s satisfies the local constraint, the X, Y positions ofthe extracted bits in the array are returned. If not, the decodingprocess fails.

FIG. 8 depicts a process that may be used to determine a location in asequence (or m-sequence) of a captured image. First, in step 801, a datastream relating to a captured image is received. In step 802,corresponding columns are extracted from A and a matrix M isconstructed.

In step 803, n independent column vectors are randomly selected from thematrix M and vector r is determined by solving equation (4). Thisprocess is performed Q times (for example, 100 times) in step 804. Thedetermination of the number of loop times is discussed in the sectionLoop Times Calculation.

In step 805, r is sorted according to its associated number of errorbits. The sorting can be done using a variety of sorting algorithms asknown in the art. For example, a selection sorting algorithm may beused. The selection sorting algorithm is beneficial when the number Q isnot large. However, if Q becomes large, other sorting algorithms (forexample, a merge sort) that handle larger numbers of items moreefficiently may be used.

The system then determines in step 806 whether error correction wasperformed successfully, by checking whether multiple r's are associatedwith the minimum number of error bits. If yes, an error is returned instep 809, indicating the decoding process failed. If not, the position sof the extracted bits in the sequence (or m-sequence) is calculated instep 807, for example, by using the Pohig-Hellman-Silver algorithm.

Next, the (X, Y) position in the array is calculated as: x=s mod m₁ andy=s mod m₂ and the results are returned in step 808.

Location Determination

FIG. 9 shows a process for determining the location of a pen tip. Theinput is an image captured by a camera and the output may be a positioncoordinates of the pen tip. Also, the output may include (or not) otherinformation such as a rotation angle of the captured image.

In step 901, an image is received from a camera. Next, the receivedimage may be optionally preprocessed in step 902 (as shown by the brokenoutline of step 902) to adjust the contrast between the light and darkpixels and the like.

Next, in step 903, the image is analyzed to determine the bit streamwithin it.

Next, in step 904, n bits are randomly selected from the bit stream formultiple times and the location of the received bit stream within theoriginal sequence (or m-sequence) is determined.

Finally, once the location of the captured image is determined in step904, the location of the pen tip may be determined in step 905.

FIG. 10 gives more details about 903 and 904 and shows the approach toextract the bit stream within a captured image. First, an image isreceived from the camera in step 1001. The image then may optionallyundergo image preprocessing in step 1002 (as shown by the broken outlineof step 1002). The pattern is extracted in step 1003. Here, pixels onthe various lines may be extracted to find the orientation of thepattern and the angle θ.

Next, the received image is analyzed in step 1004 to determine theunderlying grid lines. If grid lines are found in step 1005, then thecode is extracted from the pattern in step 1006. The code is thendecoded in step 1007 and the location of the pen tip is determined instep 1008. If no grid lines were found in step 1005, then an error isreturned in step 1009.

Outline of Enhanced Decoding and Error Correction Algorithm

With an embodiment of the invention as shown in FIG. 12, given extractedbits 1201 from a captured image (corresponding to a captured array) andthe destination area, a variation of an m-array decoding and errorcorrection process decodes the X, Y position. FIG. 12 shows a flowdiagram of process 1200 of this enhanced approach. Process 1200comprises two components 1251 and 1253.

Decode Once. Component 1251 includes three parts.

random bit selection: randomly selects a subset of the extracted bits1201 (step 1203)

decode the subset (step 1205)

determine X, Y position with local constraint (step 1209)

Decoding with Smart Bit Selection. Component 1253 includes four parts.

smart bit selection: selects another subset of the extracted bits (step1217)

decode the subset (step 1219)

adjust the number of iterations (loop times) of step 1217 and step 1219(step 1221)

determine X, Y position with local constraint (step 1225)

The embodiment of the invention utilizes a discreet strategy to selectbits, adjusts the number of loop iterations, and determines the X, Yposition (location coordinates) in accordance with a local constraint,which is provided to process 1200. With both components 1251 and 1253,steps 1205 and 1219 (“Decode Once”) utilize equation (4) to compute r.

Let {circumflex over (b)} be decoded bits, that is:{circumflex over (b)}^(t)=r^(t)M  (5)The difference between b and {circumflex over (b)} are the error bitsassociated with r.

FIG. 12 shows a flow diagram of process 1200 for decoding extracted bits1201 from a captured image in accordance with embodiments of the presentinvention. Process 1200 comprises components 1251 and 1253. Component1251 obtains extracted bits 1201 (comprising K bits) associated with acaptured image (corresponding to a captured array). In step 1203, n bits(where n is the order of the m-array) are randomly selected fromextracted bits 1201. In step 1205, process 1200 decodes once andcalculates r. In step 1207, process 1200 determines if error bits aredetected for b. If step 1207 determines that there are no error bits,X,Y coordinates of the position of the captured array are determined instep 1209. With step 1211, if the X,Y coordinates satisfy the localconstraint, i.e., coordinates that are within the destination area,process 1200 provides the X, Y position (such as to another process oruser interface) in step 1213. Otherwise, step 1215 provides a failureindication.

If step 1207 detects error bits in b, component 1253 is executed inorder to decode with error bits. Step 1217 selects another set of n bits(which differ by at least one bit from the n bits selected in step 1203)from extracted bits 1201. Steps 1221 and 1223 determine the number ofiterations (loop times) that are necessary for decoding the extractedbits. Step 1225 determines the position of the captured array by testingwhich candidates obtained in step 1219 satisfy the local constraint.Steps 1217-1225 will be discussed in more details.

Smart Bit Selection

Step 1203 randomly selects n bits from extracted bits 1201 (having Kbits), and solves for r₁. Using equation (5), decoded bits can becalculated. Let I₁={kε{1,2, . . . , K}|b_(k)={circumflex over (b)}_(k)},{overscore (I)}₁={kε{1,2, . . . , K}|b_(k)≠{circumflex over (b)}_(k)},where {circumflex over (b)}_(k) is the k^(th) bit of {circumflex over(b)}, B₁={b_(k)|kεI₁} and {overscore (B)}₁={b_(k)|kε{overscore (I)}₁},that is, B₁ are bits that the decoded results are the same as theoriginal bits, and {overscore (B)}₁ are bits that the decoded resultsare different from the original bits, I₁ and {overscore (I)}₁ are thecorresponding indices of these bits. It is appreciated that the same r₁will be obtained when any n independent bits are selected from B₁.Therefore, if the next n bits are not carefully chosen, it is possiblethat the selected bits are a subset of B₁, thus resulting in the same r₁being obtained.

In order to avoid such a situation, step 1217 selects the next n bitsaccording to the following procedure:

-   -   1. Choose at least one bit from {overscore (B)}₁ 1303 and the        rest of the bits randomly from B₁ 1301 and {overscore (B)}₁        1303, as shown in FIG. 13 corresponding to bit arrangement 1351.        Process 1200 then solves r₂ and finds B₂ 1305, 1309 and        {overscore (B)}₂ 1307, 1311 by computing {circumflex over (b)}₂        ^(t)=r₂ ^(t)M₂.    -   2. Repeat step 1. When selecting the next n bits, for every        {overscore (B)}_(i)(i=1, 2, 3 . . . , x−1, where x is the        current loop number), there is at least one bit selected from        {overscore (B)}_(i). The iteration terminates when no such        subset of bits can be selected or when the loop times are        reached.        Loop Times Calculation

With the error correction component 1253, the number of requirediterations (loop times) is adjusted after each loop. The loop times isdetermined by the expected error rate. The expected error rate p_(e) inwhich not all the selected n bits are correct is: $\begin{matrix}{p_{e} = {\left( {1 - \frac{C_{K - n_{e}}^{n}}{C_{K}^{n}}} \right)^{lt} \approx {- {\mathbb{e}}^{- {{lt}{(\frac{K - n}{K})}}^{n_{e}}}}}} & (6)\end{matrix}$where lt represents the loop times and is initialized by a constant, Kis the number of extracted bits from the captured array, n_(e)represents the minimum number of error bits incurred during theiteration of process 1200, n is the order of the m-array, and C_(K) ^(n)is the number of combinations in which n bits are selected from K bits.

In the embodiment, we want p_(e) to be less than e⁻⁵=0.0067. Incombination with (6), we have: $\begin{matrix}{{lt}_{i} = {\min\left( {{lt}_{i - 1},{\frac{5}{\left( \frac{K - n}{K} \right)^{n_{e}}} + 1}} \right)}} & (7)\end{matrix}$Adjusting the loop times may significantly reduce the number ofiterations of process 1253 that are required for error correction.Determine X, Y Position with Local Constraint

In steps 1209 and 1225, the decoded position should be within thedestination area. The destination area is an input to the algorithm, andit may be of various sizes and places or simply the whole m-arraydepending on different applications. Usually it can be predicted by theapplication. For example, if the previous position is determined,considering the writing speed, the destination area of the current pentip should be close to the previous position. However, if the pen islifted, then its next position can be anywhere. Therefore, in this case,the destination area should be the whole m-array. The correct X, Yposition is determined by the following steps.

In step 1224 process 1200 selects r_(i) whose corresponding number oferror bits is less than: $\begin{matrix}{N_{e} = \frac{\log_{10}\left( \frac{3}{lt} \right)}{{\log_{10}\left( \frac{K - n}{K} \right)} \times {\log_{10}\left( \frac{10}{lr} \right)}}} & (8)\end{matrix}$where lt is the actual loop times and lr represents the Local ConstraintRate calculated by: $\begin{matrix}{{lr} = \frac{{area}\quad{of}\quad{the}\quad{destination}\quad{area}}{L}} & (9)\end{matrix}$where L is the length of the m-array.

Step 1224 sorts r_(i) in ascending order of the number of error bits.Steps 1225, 1211 and 1212 then finds the first r_(i) in which thecorresponding X, Y position is within the destination area. Steps 1225,1211 and 1212 finally returns the X, Y position as the result (throughstep 1213), or an indication that the decoding procedure failed (throughstep 1215).

Illustrative Example of Enhanced Decoding and Error Correction Process

An illustrative example demonstrates process 1200 as performed bycomponents 1251 and 1253. Suppose n=3, K=5, I=(I₀ I₁ . . . I₆)^(t) isthe m-sequence of order n=3. Then $\begin{matrix}{A = \begin{pmatrix}I_{0} & I_{1} & I_{2} & I_{3} & I_{4} & I_{5} & I_{6} \\I_{6} & I_{0} & I_{1} & I_{2} & I_{3} & I_{4} & I_{5} \\I_{5} & I_{6} & I_{0} & I_{1} & I_{2} & I_{3} & I_{4}\end{pmatrix}} & (10)\end{matrix}$Also suppose that the extracted bits b=(b₀ b₁ b₂ b₃ b₄)^(t), where K=5,are actually the s^(th), (s+1)^(th), (s+3)^(th), (s+4)^(th), and(s+6)^(th) bits of the m-sequence (these numbers are actually modulus ofthe m-array length L=2^(n)−1=2³−1=7). Therefore $\begin{matrix}{M = \begin{pmatrix}I_{0} & I_{1} & I_{3} & I_{4} & I_{6} \\I_{6} & I_{0} & I_{2} & I_{3} & I_{5} \\I_{5} & I_{6} & I_{1} & I_{2} & I_{4}\end{pmatrix}} & (11)\end{matrix}$which consists of the 0^(th), 1^(st), 3^(rd), 4^(th), and 6^(th) columnsof A. The number s, which uniquely determines the X, Y position of b₀ inthe m-array, can be computed after solving r=(r₀ r₁ r₂)^(t) that areexpected to fulfill b^(t)=r^(t)M. Due to possible error bits in b,b^(t)=r^(t)M may not be completely fulfilled.

Process 1200 utilizes the following procedure. Randomly select n=3 bits,say {tilde over (b)}₁ ^(t)=(b₀ b₁ b₂), from b. Solving for r₁:{tilde over (b)}₁ ^(t)=r₁ ^(t){tilde over (M)}₁  (12)where {tilde over (M)}₁ consists of the 0th, 1st, and 2nd columns of M.(Note that {tilde over (M)}₁ is an n×n matrix and r₁ ^(t) is a 1×nvector so that {tilde over (b)}₁ ^(t) is a 1×n vector of selected bits.)

Next, decoded bits are computed:{circumflex over (b)}₁ ^(t)=r₁ ^(t)M  (13)where M is an n×K matrix and r₁ ^(t) is a 1×n vector so that {circumflexover (b)}₁ ^(t), is a 1×K vector. If {circumflex over (b)}₁ is identicalto b, i.e., no error bits are detected, then step 1209 determines the X,Y position and step 1211 determines whether the decoded position isinside the destination area. If so, the decoding is successful, and step1213 is performed. Otherwise, the decoding fails as indicated by step1215. If {circumflex over (b)}₁ is different from b, then error bits inb are detected and component 1253 is performed. Step 1217 determines theset B₁, say {b₀ b₁ b₂ b₃}, where the decoded bits are the same as theoriginal bits. Thus, {overscore (B)}₁={b₄} (corresponding to bitarrangement 1351 in FIG. 13). Loop times (lt) is initialized to aconstant, e.g., 100, which may be variable depending on the application.Note that the number of error bits corresponding to r₁ is equal to 1.Then step 1221 updates the loop time (lt) according to equation (7),lt₁=min(lt,13)=13.

Step 1217 next chooses another n=3 bits from b. If the bits all belongto B₁, say {b₀ b₂ b₃}, then step 1219 will determine r₁ again. In orderto avoid such repetition, step 1217 may select, for example, one bit{b₄} from {overscore (B)}₁, and the remaining two bits {b₀ b₁} from B₁.

The selected three bits form {tilde over (b)}₂ ^(t)=(b₀ b₁ b₄). Step1219 solves for r₂:{tilde over (b)}₂ ^(t)=r₂ ^(t){tilde over (M)}₂  (14)where {tilde over (M)}₂ consists of the 0^(th), 1^(st), and 4^(th)columns of M.

Step 1219 computes {circumflex over (b)}₂ ^(t)=r₂ ^(t)M. Find the setB₂, e.g., {b₀ b₁ b₄}, such that {circumflex over (b)}₂ and b are thesame. Then {overscore (B)}₂={b₂ b₃} (corresponding to bit arrangement1353 in FIG. 13). Step 1221 updates the loop times (lt) according toequation (7). Note that the number of error bits associated with r₂ isequal to 2. Substituting into (7), lt₂=min(lt₁, 32)=13.

Because another iteration needs to be performed, step 1217 choosesanother n=3 bits from b. The selected bits shall not all belong toeither B₁ or B₂. So step 1217 may select, for example, one bit {b₄} from{overscore (B)}₁, one bit {b₂} from {overscore (B)}₂, and the remainingone bit {b₀}.

The solution of r, bit selection, and loop times adjustment continuesuntil we cannot select any new n=3 bits such that they do not all belongto any previous B_(i)'s, or the maximum loop times lt is reached.

Suppose that process 1200 calculates five r_(i)(i=1,2,3,4,5), with thenumber of error bits corresponding to 1, 2, 4, 3, 2, respectively.(Actually, for this example, the number of error bits cannot exceed 2,but the illustrative example shows a larger number of error bits toillustrate the algorithm.) Step 1224 selects r_(i)'s, for example,r₁,r₂,r₄,r₅, whose corresponding numbers of error bits are less thanN_(e) shown in (8).

Step 1224 sorts the selected vectors r₁,r₂,r₄,r₅ in ascending order oftheir error bit numbers: r₁,r₂, r₅, r₄. From the sorted candidate list,steps 1225, 1211 and 1212 find the first vector r, for example, r₅,whose corresponding position is within the destination area. Step 1213then outputs the corresponding position. If none of the positions iswithin the destination area, the decoding process fails as indicated bystep 1215.

Embedded Interaction Code Recognition

Introduction to Embedded Interaction Code Recognition

As previously mentioned, to determine the location of a digital penduring interaction with one or more surfaces, images are captured by thedigital pen. FIG. 13 shows an example image. Images first undergopre-processing, and then features of effective EIC pattern in the imageare analyzed to obtain grid lines in image. Once the grid lines aredetermined, black dots on the grid lines are identified. Positions ofthe black dots help to determine which grid cells correspond to EICsymbols and which direction is the correct orientation of EIC symbols.

The grid cells formed by grid lines may or may not correspond to EICsymbols. As can be seen in FIG. 14, grid cells within the squares, whichare formed by the horizontal and vertical dashed lines in FIG. 14,correspond to EIC symbols 1400, whereas grid cells in between rows ofsymbols do not correspond to EIC symbols. In FIG. 14, the grid cell 1402is not an EIC symbol. For these reasons, a determination is made as towhich grid cells in image correspond to EIC symbols.

Correct orientation of EIC symbols is also determined. EIC symbolscaptured in image may be rotated due to pen rotation. When EIC symbolsare at the correct orientation (i.e. oriented the same as EIC symbols inEIC symbol array), the segment of EIC symbols captured in image can bematched against EIC symbol array, i.e. bits extracted from EIC symbolscan be matched against the m-array.

Once we know which grid cells correspond to EIC symbols and the correctorientation of the symbols, the EIC symbols captured in an image arerecognized. We then consider a large enough section 1404 of EIC symbolarray that encompasses the grid lines and corresponding EIC symbols ofthe image.

In FIG. 14, X, Y is the coordinate system (referenced generally as 1412in FIG. 14) of the image, with the image center as the origin, andpixels as the unit of measure. The X, Y coordinate system 1412 isdetermined in relation to the image, i.e. facing the image, X is left toright and Y is top to bottom.

H′, V′ is the coordinate system (referenced generally as 1410 in FIG.14) of the grid, with the top (relative to image) intersection point ofthe farthest grid lines in image, C_(H′V′), as the origin, and gridcells as the unit of measure. The H′, V′ coordinate system 1410 isdetermined in relation to the image. The rotation angle from X to H′ issmaller than that from X to V′, and intersections of grid lines in imagehave non-negative coordinates in the H′, V′ coordinate system 1410.

What is depicted inside the image in FIG. 14 should not be thought of aswhat a real image may look like. Grid lines are typically not seen inimage. But if we assume a perspective transform from paper to image,effective EIC pattern in image may appear to lie on grid lines that area perspective transform of the grid lines in EIC symbol array (i.e., thediagonal lines in FIG. 14). Therefore, we can draw grid lines in imageand the H′, V′ coordinate system 1410 based on a perspective transformof the grid lines in EIC symbol array 1406.

X′, Y′ is the coordinate system (referenced generally as 1408 in FIG.14) of the section 1404 of EIC symbol array encompassing the grid linesand corresponding EIC symbols of the image, with the top-left corner ofthe section, C_(X′Y′), as the origin, and EIC symbols as the unit ofmeasure. X′, Y′ is in the direction of EIC symbol array, and the originis at the top-left corner of a symbol.

FIG. 15 shows the three coordinate systems of another image (which maybe thought of as taken after the pen is moved and rotated). Thecoordinate systems of X, Y 1412 and H′, V′ 1410 stay in relation to theimage. The coordinate system of X′, Y′ 1408 is in the direction of EICsymbol array 1406. Therefore, the rotation from H′, V′ to X′, Y′ now is$- \frac{\pi}{4}$whereas it was $- \frac{\pi}{4}$in FIG. 15.

Given a particular EIC symbol design, and the identified correctorientation of EIC symbols in an image, a transformation from thesection 1404 of EIC symbol array (that encompasses the grid lines andcorresponding EIC symbols of the image) to grid, i.e. from X′, Y′ to H′,V′, can be obtained. For example, with EIC symbol 8-a-16 (FIG. 26A), thescale from the unit of measure in H′, V′ to that of X′, Y′ is √{squareroot over (2)}, and the rotation from H′, V′ to X′, Y′ may be${- \frac{\pi}{4}},\frac{\pi}{4},\frac{3\pi}{4},{{or}{\quad\quad}\frac{5\pi}{4}},$depending on the correct orientation of EIC symbols in image (FIGS. 14and 15 show two of these situations). We refer to the homography matrixdescribing the transformation from X′, Y′ to H′, V′ as H_(Symbol→Grid).

From a previous step, a homography matrix describing the perspectivetransform from grid to image, i.e. from H′, V′ to X, Y, H_(Grid→Image),is known. Herein we assume digital pen is used on a plane (such as apaper plane where EIC pattern is printed on) and the spatialtransformation from the plane to image (also assumed a plane) is aperspective transform. That is, effective EIC pattern in image shouldlie on grid lines that are a perspective transform of the grid lines inEIC symbol array. The perspective transform is first assumed to be anaffine transform, i.e. evenly spaced parallel lines are kept evenlyspaced and parallel, but perpendicular lines may not be perpendicularanymore. Rotation, scale and translation of the affine transform areestimated from analyzing effective EIC pattern in image. The perspectivetransform is then obtained by fitting effective EIC pattern to affinetransformed grid lines. A homography matrix H_(Grid→Image) thatdescribes the perspective transform from grid lines in EIC symbol arrayto image is obtained.

Thus, a homography matrix, H_(Symbol →Image), describing thetransformation from X′, Y′ to X, Y can be obtained as:H _(Symbol→Image) =H _(Grid→Image) ·H _(Symbol→Grid)

The homography matrix H_(Symbol→Image) specifies the transformation ofpoints in the section 1404 of EIC symbol array encompassing the image toa point in the image coordinate system 1412. The homography matrixH_(Symbol→Image) ⁻¹, specifies the transformation of each point in theimage coordinate system 1412 to a point in the section 1404 of EICsymbol array encompassing the image.

From recognized EIC symbols in the section of EIC symbol arrayencompassing the image, EIC bits are extracted. For each m-array, astream of bits is extracted. Any bit can be chosen as the bit whoseposition in m-array is decoded.

For convenience, we choose the top-left corner of the section 1404 ofEIC symbol array encompassing the image, C_(X′Y′), as the position todecode. In the bit stream starting from C_(X′Y′), some of the bits areknown (bits extracted from recognized symbols), and some are unknown(bits that can't be extracted or EIC symbols are not captured in image).As long as the number of extracted bits is more than the order of them-array, decoding can be done.

We call this process EIC symbol recognition. FIG. 16 shows a flowdiagram of a system for performing EIC symbol recognition in accordancewith embodiments of the invention.

From EIC pattern analysis, H_(Grid→Image) is obtained, with which gridlines in image are obtained. Grid cells thus obtained are effective EICsymbols. Given effective EIC symbols, the next step is to recognize thesymbols. The goal of EIC symbol recognition is to obtain bits encoded inEIC symbols and obtain a homography matrix H_(Symbol→Image), whichdescribes the transformation from the section of EIC symbol arrayencompassing the image to image. Input of EIC symbol recognition ishomography matrix obtained from EIC pattern analysis H_(Grid→Image),normalized image, and document content mask. Example input to EIC symbolrecognition is shown in FIG. 17. Output of EIC symbol recognition isextracted bits (and confidence values of the bits) and homography matrixH_(Symbol→Image). FIG. 18 shows example recognized EIC bits andcorresponding confidence values for the recognized EIC bits.

The EIC symbol recognition system shown in FIG. 16 includes anEIC-dot-detection module 1604, an EIC-symbol-orientation-determinationmodule 1612, and an EIC-bit-extraction module 1616, each of which isdescribed in more detail below.

EIC Dot Detection

The EIC-dot-detection module 1604 detects black dots on each edge.First, we move the origin of H, V to get the H′, V′ coordinate system.By moving the origin of H, V, all grid intersections in the image havenon-negative coordinates. We call the new coordinate system H′, V′, asshown in FIG. 19.

Suppose C′ has coordinates (h′,v′) in H, V coordinate system. Aftermoving, its coordinates are (0, 0).

Suppose the homography matrix obtained from EIC pattern analysis is:$H = \begin{bmatrix}h_{11} & h_{12} & h_{13} \\h_{21} & h_{22} & h_{23} \\h_{31} & h_{32} & h_{33}\end{bmatrix}$

The homography matrix that transforms a point in the H′, V′ coordinatesystem to a point in the X, Y coordinate system is: $H = \begin{bmatrix}h_{11} & h_{12} & {h_{13} + {h_{11} \cdot {h'}} + {h_{12} \cdot v^{\prime}}} \\h_{21} & h_{22} & {h_{23} + {h_{21} \cdot {h'}} + {h_{22} \cdot v^{\prime}}} \\h_{31} & h_{32} & {h_{33} + {h_{31} \cdot {h'}} + {h_{32} \cdot v^{\prime}}}\end{bmatrix}$

This homography matrix is referred to herein as the finalH_(Grid→Image).

With homography matrix H_(Grid→Image), all the grid lines in image areobtained (by transforming the grid lines in EIC symbol array using thehomography matrix) and form the H′, V′ coordinate system, as shown inFIG. 20.

These grid lines are referred to as H lines and V lines. Grid cells areindexed by the H′, V′ coordinates of the top corner of the cell. Edgesof the cells are identified as either on the H lines or on the V lines.For example, in FIG. 20, the cell (i, j) has two edges: edge h, i, j andedge v, i, j.

Next, graylevels are obtained of selected positions on each edge. ForEIC symbol 8-a-16, for example, there are 5 EIC dot positions on eachedge, as shown in FIG. 21. The EIC symbol in FIG. 21 occupies all of therows and columns of grid spaces shown in FIG. 21 except for the bottomrow and the right-most column. That row and that column belong toadjacent EIC symbols. Accordingly, while black dots 2102-1 and 21024belong to the EIC symbol shown in FIG. 21, black dots 2102-2 and 2102-3are not part of that EIC symbol. There are EIC data dot positions andEIC orientation dot positions. Data dots 2106-1 through 2106-16 may beblack or white for representing bits of information. Of the 4 data dotpositions on each edge, there may be only one black dot. Orientationdots 2104-1 through 2104-4 are always white to facilitate properlyorienting camera-captured EIC-symbol images.

Graylevels of the 5 positions on each edge, as shown in FIG. 20, areobtained. First, coordinates of the positions in the H′, V′ coordinatesystem are obtained. Suppose the total number of H lines is N_(h)+1, andthe total number of V lines is N_(v)+1. For each position s on each edge(i, j) on the H line, where s=1, 2, . . . , 5, i=0, 1, . . . , N_(h)−1,j=0, 1, . . . , N_(v), the H′, V′ coordinates are:$\left( {{i + \frac{s + 1}{8}},j,1} \right)^{t}.$For each position s on each edge (i, j) on the V line, where s=1, 2, . .. , 5, i=0, 1, . . . N_(h), j=0, 1, . . . , N_(v)−1, the H′, V′coordinates are: $\left( {i,{j + \frac{s + 1}{8}},1} \right)^{t}.$

Next, with the homography matrix H_(Grid→Image), coordinates of thepositions in the X, Y coordinate system are obtained. For each positions on each edge (i, j) on the H line, where s=1, 2, . . . , 5, i=0, 1, .. . , N_(h)−1, j=0, 1, . . . , N_(v), the X, Y coordinates are: (x_(s)^(h,i,j), y_(x) ^(h,i,j), 1)^(t)=H_(Grid→Image)$\left( {{i + \frac{s + 1}{8}},j,1} \right)^{t}.$For each position s on each edge (i, j) on the V line, where s=1, 2, . .. , 5, i=0, 1, . . . , N_(h), j=0, 1, . . . , N_(v)−1, the X, Ycoordinates are: (x_(s) ^(v,i,j),y_(s) ^(v,i,j),1)^(t)=H_(Grid→Image)$\left( {i,{j + \frac{s + 1}{8}},1} \right)^{t}$

Graylevels of the positions are calculated using bilinear sampling ofthe pixels surrounding the positions. For each position s on edge (i, j)on the H line, where s=1, 2, . . . , 5, i=0, 1, . . . , N_(h)−1, j=0, 1,. . . , N_(v), get the index of the first pixel for bilinear sampling:x₁≈int(x_(s) ^(h,i,j)+63.5), y₁=int(y_(s) ^(h,i,j)+49.5).

If

-   -   0≦x₁≦126    -   0≦y₁≦98    -   Document Content Mask (x₁, y₁)=0    -   Document Content Mask (x₁+1, y₁)=0    -   Document Content Mask (x₁,y₁+1)=0    -   Document Content Mask (x₁+1,y₁+1)=0

then,

-   -   The position is valid.    -   η_(x)=decimal(x_(s) ^(h,i,j)+63.5)    -   η_(y)=decimal(y_(s) ^(h,i,j)+49.5)    -   G_(s) ^(h,i,j)=(1−η_(y))·[(1−η_(x))·G_((x) ₁ _(,y) ₁        ₎+η_(x)·G_(x) ₁ _(+1,y) ₁ ₎]+η_(y)·[(1−η_(x))·G_((x) ₁ _(,y) ₁        ₊₁₎+η_(x)·G_((x) ₁ _(+1,y) ₁ ₊₁₎]

else,

-   -   The position is not valid.    -   G_(s) ^(h,i,j)=null.

The function decimal(x) returns the decimal fraction part of x, wherex≧0. For example, decimal(1.8)=0.8. (x₁,y₁), (x₁+1,y₁), (x₁,y₁+1) and(x₁+1,y₁+1) are indexes of the pixels used for bilinear sampling,defined by the coordinate system shown in FIG. 22. FIG. 23 shows anillustration of the pixels used for bilinear sampling.

Similarly, for each position s on edge (i, j) on the V line, where s=1,2, . . . , 5, i=0, 1, . . . , N_(h), j=0, 1, . . . , N_(v)−1, get theindex of the first pixel for bilinear sampling:

-   -   x₁=int(x_(s) ^(v,i,j)+63.5)    -   y₁=int(y_(s) ^(v,i,j)+49.5)

If

-   -   0≦x₁≦126    -   0≦y₁≦98    -   Document Content Mask (x₁,y₁)=0    -   Document Content Mask (x₁+1,y₁)=0    -   Document Content Mask (x₁, y₁+1)=0    -   Document Content Mask (x₁+1,y₁+1)=0

then,

-   -   The position is valid.    -   η_(x)=decimal(x_(s) ^(v,i,j)+63.5)    -   η_(y)=decimal(y_(s) ^(v,i,j)+49.5)    -   G_(s) ^(v,i,j)=(1−η_(y))·[(1−η_(x))·G_((x) ₁ _(,y) ₁        ₎+η_(x)·G_(x) ₁ _(+1,y) ₁ ₎]+η_(y)·[(1−η_(x))·G_((x) ₁ _(,y) ₁        ₊₁₎+η_(x)·G_((x) ₁ _(+1,y) ₁ ₊₁₎]

else,

-   -   The position is not valid.    -   G_(s) ^(v,i,j)=null

Next, black dots are detected.

Based on the relative graylevels of the positions, black dots aredetermined. First, the five positions on each edge are named as follows(see FIG. 24):

-   -   he_(s) ^(i,j)|s=1, 2, . . . , 5 when the edge is on an H line        and mod(i+j,2)=0;    -   ho_(s) ^(i,j)|s=1, 2, . . . , 5 when the edge is on an H line        and mod(i+j,2)=1;    -   ve_(s) ^(i,j)|s=1, 2, . . . , 5 when the edge is on a V line and        mod(i+j,2)=0;    -   vo_(s) ^(i,j)|s=1, 2, . . . , 5 when the edge is on a V line and        mod(i+j,2)=1.

For each edge, let the count of valid positions be VD^(k,i,j), wherek=h, v. If there are at least two valid positions on an edge, i.e.VD^(k,i,j)≧2, let$u_{1} = {\underset{1 \leq s \leq 5}{{Arg}\quad{Min}}G_{s}^{k,i,j}}$and$u_{2} = {\underset{{1 \leq s \leq 5},{s \neq u_{1}}}{{Arg}\quad{Min}}G_{s}^{k,i,j}}$i.e., u₁ is the darkest position and u₂ is the second darkest position.If the graylevel difference between the darkest and the second darkestposition is large enough, i.e. exceeds a threshold (e.g., T₀=20), thedarkest position is considered a black dot.

For each edge (i, j) on the H line, where i=0, 1, . . . , N_(h)−1, j=0,1, . . . , N_(v) and mod(i+j,2)=0,

-   -   If (G_(u) ₂ ^(h,i,j)−G_(u) ₁ ^(h,i,j))>T₀, then,        -   he_(u) ₁ ^(i,j)=1, where 1≦u₁≦5        -   he_(s) ^(i,j)=0, where s=1, 2, . . . , 5 and s≠u₁        -   D_(s) ^(h,i,j)=he_(s) ^(i,j)        -   Diff^(h,i,j)=G_(u) ₂ ^(h,i,j)−G_(u) ₁ ^(h,i,j)    -   else,        -   he_(s) ^(i,j)=0, where s=1, 2, . . . , 5        -   D_(s) ^(h,i,j)=null        -   Diff^(h,i,j)=null

For each edge (i, j) on the H line, where i=0, 1, . . . , N_(h)−1, j=0,1, . . . , N_(v) and mod(i+j,2)=1,

-   -   If (G_(u) ₂ ^(h,i,j)−G_(u) ₁ ^(h,i,j))>T₀, then,        -   ho_(u) ₁ ^(i,j)=1, where 1≦u₁≦5        -   ho_(s) ^(i,j)=0, where s=1, 2, . . . , 5 and s≠u₁        -   D_(s) ^(h,i,j)=ho_(s) ^(i,j)        -   Diff^(h,i,j)=G_(u) ₂ ^(h,i,j)−G_(u) ₁ ^(h,i,j)    -   else,        -   ho_(s) ^(i,j)=0, where s=1, 2, . . . , 5        -   D_(s) ^(h,i,j)=null        -   Diff^(h,i,j)=null

For each edge (i, j) on the V line, where i=0, 1, . . . , N_(h), j=0, 1,. . . , N_(v)−1 and mod(i+j,2)=0,

-   -   If (G_(u) ₂ ^(v,i,j)−G_(u) ₁ ^(v,i,j))>T₀, then,        -   ve_(u) ₁ ^(i,j)=1, where 1≦u₁≦5        -   ve_(s) ^(i,j)=0, where s=1, 2, . . . , 5 and s≠u₁        -   D_(s) ^(v,i,j)=ve_(s) ^(i,j)        -   Diff^(v,i,j)=G_(u) ₂ ^(v,i,j)−G_(u) ₁ ^(v,i,j)    -   else,        -   ve_(s) ^(i,j)=0, where s=1, 2, . . . , 5        -   D_(s) ^(v,i,j)=null        -   Diff^(v,i,j)=null

For each edge (i, j) on the V line, where i=0, 1, . . . , N_(h), j=0, 1,. . . , N_(v)−1 and mod(i+j,2)=1,

-   -   If (G_(u) ₂ ^(v,i,j)−G_(u) ₁ ^(v,i,j))>T₀, then,        -   vo_(u) ₁ ^(i,j)=1, where 1≦u₁≦5        -   vo_(s) ^(i,j)=0, where s=1, 2, . . . , 5 and s≠u₁        -   D_(s) ^(v,i,j)=vo_(s) ^(i,j)        -   Diff^(v,i,j)=G_(u) ₂ ^(v,i,j)−G_(u) ₁ ^(v,i,j)    -   else,        -   vo_(s) ^(i,j)=0, where s=1, 2, . . . , 5        -   D_(s) ^(v,i,j)=null        -   Diff^(v,i,j)=null

By now, substantially all of the black dots are detected. he_(s) ^(i,j),ho_(s) ^(i,j), ve_(s) ^(i,j) and vo_(s) ^(i,j) will be used to determinewhich grid cells correspond to EIC symbols and the correct orientationof the symbols. D_(s) ^(h,i,j) and D_(s) ^(v,i,j) will be used for bitextraction.

EIC Symbol Orientation Determination

Now that the black dots are detected, theEIC-symbol-orientation-determination module 1612, which accepts EIC dots1610 as input, determines which grid cells correspond to EIC symbols andwhich direction is the correct orientation of the symbols, asillustrated in FIG. 25.

Recall that the orientation dot positions are designed to help todetermine the correct orientation of a symbol. When EIC symbols arerotated, the location of the orientation dot positions are different, asillustrated in FIGS. 26A-D. FIG. 26A shows the symbol shown in FIG. 21.FIG. 26B shows the symbol rotated 90 degrees clockwise. FIG. 26C showsthe symbol rotated 180 degrees clockwise. FIG. 26D shows the symbolrotated 270 degrees clockwise.

Since there should be no black dots at orientation dot positions, thetotal number of detected black dots at orientation dot positionsassuming no rotation, rotated 90 degrees clockwise, rotated 180 degreesclockwise, and rotated 270 degrees clockwise, can be obtained. Theassumption (of a correct orientation) is accepted if the total countunder the assumption is the smallest.

Therefore, the EIC-symbol-orientation-determination module first obtainsthe total number of black dots at orientation dot positions underdifferent assumptions about which grid cells correspond to EIC symbolsand the correct orientation of the symbols. Then, based on the smallestcount, which grid cells correspond to EIC symbols and the correctorientation of the symbols are determined.

The section of EIC symbol array encompassing the image, i.e. the X′, Y′coordinate system discussed above in connection with FIG. 15, is thendetermined. A homography matrix H_(Symbol→Grid), which describes thetransformation from the section of EIC symbol array encompassing theimage to grid, i.e. from the X′, Y′ coordinate system, to the H′, V′coordinate system, can be obtained.

Finally, given H_(Symbol→Grid) and H_(Grid→Image) obtained from EICpattern analysis, a homography matrix H_(Symbol→Image), which describesthe transformation from the section of EIC symbol array encompassing theimage to image, i.e. from the X′, Y′ coordinate system 1408 to the X, Ycoordinate system 1412, is obtained.

The total number of black dots at orientation dot positions isdetermined as follows.

Let$Q_{0} = {{\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{he}_{5}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ho}_{5}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ve}_{5}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{vo}_{1}^{i,j}}}}$$Q_{1} = {{\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{he}_{1}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ho}_{5}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ve}_{5}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{vo}_{5}^{i,j}}}}$$Q_{2} = {{\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{he}_{1}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ho}_{1}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ve}_{5}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{vo}_{1}^{i,j}}}}$$Q_{3} = {{\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{he}_{1}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ho}_{5}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ve}_{1}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{vo}_{1}^{i,j}}}}$$Q_{4} = {{\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{he}_{5}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ho}_{5}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ve}_{1}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{vo}_{5}^{i,j}}}}$$Q_{5} = {{\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{he}_{5}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ho}_{1}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ve}_{5}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{vo}_{5}^{i,j}}}}$$Q_{6} = {{\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{he}_{1}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ho}_{1}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ve}_{1}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{vo}_{5}^{i,j}}}}$$Q_{7} = {{\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{he}_{5}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ho}_{1}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{ve}_{1}^{i,j}}} + {\sum\limits_{i = 0}^{N_{h}}{\sum\limits_{j = 0}^{N_{v}}{vo}_{1}^{i,j}}}}$

Here Q_(i), where i=1, 2, . . . , 7, represent the total number ofdetected black dots at orientation dot positions, given differentassumptions about which grid cells correspond to EIC symbols and thecorrect orientation of the symbols.

Q₀ is the total number of detected black dots at orientation dotpositions if grid cell (i, j) is a symbol and (i, j) is the top cornerof the symbol (assuming mod(i+j,2)=0, see FIG. 24). Q₁ is the totalnumber of detected black dots at orientation dot positions if grid cell(i, j) is a symbol, and (i+1, j) is the top corner of the symbol. Q₂ isthe total number of detected black dots at orientation dot positions ifgrid cell (i, j) is a symbol, and (i+1, j+1) is the top corner of thesymbol. Q₃ is the total number of detected black dots at orientation dotpositions if grid cell (i, j) is a symbol, and (i, j+1) is the topcorner of the symbol.

Q₄ is the total number of detected black dots at orientation dotpositions if grid cell (i+1, j) is a symbol, and (i+1, j) is the topcorner of the symbol. Q₅ is the total number of detected black dots atorientation dot positions if grid cell. (i+1, j) is a symbol, and (i+2,j) is the top corner of the symbol. Q₆ is the total number of detectedblack dots at orientation dot positions if grid cell (i+1, j) is asymbol, and (i+2, j+1) is the top corner of the symbol. Q₇ is the totalnumber of detected black dots at orientation dot positions if grid cell(i+1, j) is a symbol, and (i+1, j+1) is the top corner of the symbol.

Next, determinations are made with respect to which grid cellscorrespond to EIC symbols and what the correct orientation is for thesymbols.${{Let}\quad j} = {\underset{0 \leq i \leq 7}{{Arg}\quad{Min}}{\left( Q_{i} \right).}}$

Let O=int(j/4). O represents which grid cells correspond to EIC symbols.If O=0, grid cell (0, 0) is a symbol. If O=1, grid cell (1, 0) is asymbol. See FIG. 27. Here, we call O an offset.

Let Q=mod(j,4). Q represents the correct orientation of the symbols. EICsymbols in image are rotated $Q \cdot \frac{\pi}{2}$clockwise.

Next, the homography matrix, which transforms symbol to image, isobtained.

Now that we know which grid cells correspond to EIC symbols and thecorrect orientation of the symbols, the section of EIC symbol arrayencompassing the image, i.e. the X′, Y′ coordinate system 1408, can bedetermined. And the homography matrix H_(Symbol→Grid), which describesthe transformation from X′, Y′ 1408 to H′, V′ 1410, is obtained.

First, we introduce the H″, V″ coordinate system. H″, V″ is H′, V′rotated, with the origin moved to the corner of the grid lines thatcorrespond to the top corner of a symbol.

When Q=0, the top corner of the H′, V′ grid lines corresponds to the topcorner of a symbol. H″, V″ is the same as H′, V′. X′, Y′ is the sectionof EIC symbol array encompassing the image. See FIG. 28, which assumesO=1 and which shows symbol, grid, and image coordinate systems when Q=0.

When Q=1, the far right corner of the H′, V′ grid lines corresponds tothe top corner of a symbol. H″, V″ is H′, V′ rotated 90 degreesclockwise, with the origin moved to the far right corner of the H′, V′grid lines. X′, Y′ is the section of EIC symbol array encompassing theimage. See FIG. 29, which shows symbol, grid, and image coordinatesystems when Q=1.

When Q=2, the bottom corner of the H′, V′ grid lines corresponds to thetop corner of a symbol. H″, V″ is H′, V′ rotated 180 degrees clockwise,with the origin moved to the bottom corner of the H′, V′ grid lines. X′,Y′ is the section of EIC symbol array encompassing the image. See FIG.30, which shows symbol, grid, and image coordinate systems when Q=2.

When Q=3, the far left corner of the H′, V′ grids corresponds to the topcorner of a symbol. H″, V″ is H′, V′ rotated 270 degrees clockwise, withthe origin moved to the far left corner of the H′, V′ grid lines. X′, Y′is the section of EIC symbol array encompassing the image. See FIG. 31,which shows symbol, grid, and image coordinate systems when Q=3.

Let the rotation angle from H′, V′ to H″, V″ be θ_(Q):${\theta_{Q} = {Q \cdot \frac{\pi}{2}}},{{i.e.\quad\theta_{Q}} \in {\left\{ {0,\frac{\pi}{2},\pi,\frac{3\pi}{2}} \right\}.}}$

Let θ_(s) be the angle from H′, V′ to X′, Y′:${\theta_{s} = {{Q \cdot \frac{\pi}{2}} - \frac{\pi}{4}}},{{i.e.\quad\theta_{s}} \in {\left\{ {{- \frac{\pi}{4}},\frac{\pi}{4},\frac{3\quad\pi}{4},\frac{5\pi}{4}} \right\}.}}$

Let the origin of the H″, V″ coordinate system, C_(H″V″), have thecoordinates (h′_(C) _(H″V″) ,v′_(C) _(H″V″) ) in H′, V′ coordinates. Wethen have,${h_{C_{H{{}_{}^{}{}_{}^{}}}}^{\prime} = {{{int}\left( \frac{{mod}\left( {{Q + 1},4} \right)}{2} \right)} \cdot N_{h}}},{v_{C_{H^{\prime\prime}V^{\prime\prime}}}^{\prime} = {{{int}\left( \frac{{mod}\left( {Q,4} \right)}{2} \right)} \cdot {N_{v}.}}}$

Let the transform from H″, V″ to H′, V′ be ΔH_(Q), i.e. $\begin{bmatrix}h^{\prime} \\v^{\prime} \\1\end{bmatrix} = {\Delta\quad{H_{Q} \cdot {\begin{bmatrix}h^{\prime\prime} \\v^{\prime\prime} \\1\end{bmatrix}.}}}$

We will have, ${\Delta\quad H_{Q}} = {\begin{pmatrix}{\cos\quad\theta_{Q}} & {{- \sin}\quad\theta_{Q}} & h_{C_{H^{\prime\prime}V^{\prime\prime}}}^{\prime} \\{\sin\quad\theta_{Q}} & {\cos\quad\theta_{Q}} & v_{C_{H^{\prime\prime}V^{\prime\prime}}}^{\prime} \\0 & 0 & 1\end{pmatrix}.}$

Now, ΔH₀ is obtained. ΔH₀ is the transform from X′, Y′ to H″, V″, i.e.$\begin{bmatrix}h^{\prime\prime} \\v^{\prime\prime} \\1\end{bmatrix} = {\Delta\quad{H_{0} \cdot {\begin{bmatrix}x^{\prime} \\y^{\prime} \\1\end{bmatrix}.}}}$

Let O₀ be the offset in H″, V″ coordinate system. We will have,$O_{0} = \left\{ {\begin{matrix}{{O,{{{if}\quad Q} = 0}}\quad} \\{{{mod}\left( {{N_{h} + O + 1},2} \right)},{{{if}\quad Q} = 1}} \\{{{mod}\left( {{N_{h} + N_{v} + O},2} \right)},{{{if}\quad Q} = 2}} \\{{{mod}\left( {{N_{v} + O + 1},2} \right)},{{{if}\quad Q} = 3}}\end{matrix}.} \right.$

Let N_(h) ⁰+1 and N_(v) ⁰+1 be the total number of H and V lines in H″,V″ coordinate system. We will have, $N_{h}^{0} = \left\{ {\begin{matrix}{N_{h},{{{if}\quad Q} = 0}} \\{N_{v},{{{if}\quad Q} = 1}} \\{N_{h},{{{if}\quad Q} = 2}} \\{N_{v},{{{if}\quad Q} = 3}}\end{matrix},{N_{v}^{0} = \left\{ {\begin{matrix}{N_{v},{{{if}\quad Q} = 0}} \\{N_{h},{{{if}\quad Q} = 1}} \\{N_{v},{{{if}\quad Q} = 2}} \\{N_{h},{{{if}\quad Q} = 3}}\end{matrix}.} \right.}} \right.$

Let the origin of the X′, Y′ coordinate system, C_(X′Y′), have thecoordinates (h″_(C) _(X′Y′) ,v″_(C) _(X′Y′) ) in the H″, V″ coordinatesystem:${h_{C_{X^{\prime}Y^{\prime}}}^{\prime\prime} = {{- {{int}\left( \frac{N_{v}^{0} + O_{0}}{2} \right)}} - \frac{1}{2}}},{v_{C_{X^{\prime}Y^{\prime}}}^{\prime\prime} = {{{int}\left( \frac{N_{v}^{0} + O_{0}}{2} \right)} + \frac{1}{2} - {O_{0}.}}}$

Since the rotation from H″, V″ to X′, Y′ is −π/4, and the scale is√{square root over (2)} from the unit of measure in H″, V″ to X′, Y′, wewill have, ${\Delta\quad H_{0}} = {\begin{pmatrix}{{\sqrt{2}\cos} - \frac{\pi}{4}} & {{{- \sqrt{2}}\sin} - \frac{\pi}{4}} & h_{C_{X^{\prime}Y^{\prime}}}^{\prime\prime} \\{{\sqrt{2}\cos} - \frac{\pi}{4}} & {{\sqrt{2}\cos} - \frac{\pi}{4}} & v_{C_{X^{\prime}Y^{\prime}}}^{\prime\prime} \\0 & 0 & 1\end{pmatrix} = {\begin{pmatrix}1 & 1 & h_{C_{X^{\prime}Y^{\prime}}}^{\prime\prime} \\{- 1} & 1 & v_{C_{X^{\prime}Y^{\prime}}}^{\prime\prime} \\0 & 0 & 1\end{pmatrix}.}}$

Therefore, the transform from X′, Y′ to H′, V′ is:H _(Symbol→Grid) =ΔH _(Z) ·ΔH ₀.

From EIC pattern analysis, H_(Grid→Image) is obtained, i.e.$\begin{bmatrix}x \\y \\1\end{bmatrix} = {H_{{Grid}\rightarrow{Image}} \cdot {\begin{bmatrix}h^{\prime} \\v^{\prime} \\1\end{bmatrix}.}}$

Therefore, a transform from the coordinate system of the section of EICsymbol array encompassing the image (X′, Y′ coordinate system) to thecoordinate system of the image (the X, Y coordinate system),H_(Symbol→Image) can be obtained: ${\begin{bmatrix}x \\y \\1\end{bmatrix} = {{H_{{Grid}\rightarrow{Image}} \cdot \begin{bmatrix}h^{\prime} \\v^{\prime} \\1\end{bmatrix}} = {H_{{Grid}\rightarrow{Image}} \cdot H_{{Symbol}\rightarrow{Grid}} \cdot \begin{bmatrix}x^{\prime} \\y^{\prime} \\1\end{bmatrix}}}},$i.e.,H _(Symbol→Image) =H _(Grid→Image) ·H _(Symbol→Grid).

An output of this step is H_(Symbol→Image), i.e. the updated homographymatrix with orientation information 1622 in FIG. 16. As explained above,we can estimate the orientation and offset of actual EIC symbols.Rotated EIC Dots 1614 and updated homography matrix with orientationinformation 1622 are the two aspects of the estimation. Based on thehomography matrix without orientation information obtained in previousstep and orientation & offset estimation, 1622 is obtained. Based on theorientation & offset estimation, we can rotate the EIC dots andassociate them with EIC symbols, thus based on this result we canrecognize the information embedded in each EIC symbol respectively.

Rotated EIC Dots 1614 (i.e., D₀ and Diff₀) are also output of 1612 inFIG. 16. First, we obtain positions of black dots on each edge in H″, V″coordinate system, based on the positions of black dots in H′, V′coordinate system. We also obtain the graylevel difference of thedarkest and the second darkest positions on each edge. Note that theedges are now named based on coordinates of intersection points in H″,V″ coordinate system.

For each position s on edge (i, j) on the H line in H″, V″ coordinatesystem, where s=1, 2, . . . , 5, i=0, 1, . . . , N_(h) ⁰−1, j=0, 1, . .. , N_(v) ⁰, $D_{0,s}^{h,i,j} = \left\{ {\begin{matrix}{D_{s}^{h,i,j},{{{if}\quad Q} = 0}} \\{D_{s}^{v,{N_{v}^{0} - j},i},{{{if}\quad Q} = 1}} \\{D_{6 - s}^{h,{N_{h}^{0} - i - 1},{N_{v}^{0} - j}},{{{if}\quad Q} = 2}} \\{D_{6 - s}^{v,j,{N_{h}^{0} - i - 1}},{{{if}\quad Q} = 3}}\end{matrix},{{Diff}_{0}^{h,i,j} = \left\{ {\begin{matrix}{{Diff}^{h,i,j},{{{if}\quad Q} = 0}} \\{{Diff}^{v,{N_{v}^{0} - j},i},{{{if}\quad Q} = 1}} \\{{Diff}^{h,{N_{h}^{0} - i - 1},{N_{v}^{0} - j}},{{{if}\quad Q} = 2}} \\{{Diff}^{v,j,{N_{h}^{0} - i - 1}},{{{if}{\quad\quad}Q} = 3}}\end{matrix}.} \right.}} \right.$

For each position s on edge (i, j) on the V line in H″, V″ coordinatesystem, where s=1, 2, . . . , 5, i=0, 1, . . . , N_(h) ⁰, j=0, 1, . . ., N_(v) ⁰−1, $D_{0,s}^{v,i,j} = \left\{ {\begin{matrix}{D_{s}^{v,i,j},{{{if}\quad Q} = 0}} \\{D_{6 - s}^{h,{N_{v}^{0} - j - 1},i},{{{if}\quad Q} = 1}} \\{D_{6 - s}^{v,{N_{h}^{0} - i},{N_{v}^{0} - j - 1}},{{{if}\quad Q} = 2}} \\{D_{s}^{h,j,{N_{h}^{0} - i}},{{{if}\quad Q} = 3}}\end{matrix},{{Diff}_{0}^{v,i,j} = \left\{ {\begin{matrix}{{Diff}^{v,i,j},{{{if}\quad Q} = 0}} \\{{Diff}^{h,{N_{v}^{0} - j - 1},i},{{{if}\quad Q} = 1}} \\{{Diff}^{v,{N_{h}^{0} - i},{N_{v}^{0} - j - 1}},{{{if}\quad Q} = 2}} \\{{Diff}^{h,j,{N_{h}^{0} - i}},{{{if}{\quad\quad}Q} = 3}}\end{matrix}.} \right.}} \right.$

Recall that 2 bits are encoded on each edge of an EIC symbol. Let B_(l)^(h,i,j) and B_(l) ^(v,i,j) be the two bits, where l=0, 1.

EIC Bit Extraction

Now that it is known which grid cells correspond to EIC symbols and thecorrect orientation of the symbols, bits can be extracted based on thepositions of black dots on each edge of a symbol. The EIC-bit-extractionmodule 1616 takes as input the rotated EIC dots 1614 and produces EICbits 1620.

Bit extraction is done in H″, V″ coordinate system, i.e. EIC symbols areoriented at the correct orientation.

For each edge, if there is a black dot detected, and all 5 positions onthe edge are valid, bits are extracted. Otherwise, bits are notextracted.

For each edge (i, j) on the H line in H″, V″ coordinate system, wherei=0, 1, . . . , N_(h) ⁰−1, j=0, 1, . . . , N_(v) ⁰,

If there exists w and D_(0,w) ^(h,i,j)=1, where wε{1,2,3,4}, andVD^(h,i,j)=5, then,${B_{0}^{h,i,j} = {{int}\left( \frac{{mod}\left( {w,4} \right)}{2} \right)}},{B_{1}^{h,i,j} = {{int}\left( \frac{w - 1}{2} \right)}},$

else,

-   -   B₀ ^(h,i,j)=B₁ ^(h,i,j)=null.

Similarly, for each edge (i, j) on the V line in H″, V″ coordinatesystem, where i=0, 1, . . . , N_(h) ⁰, j=0, 1, . . . , N_(v) ⁰−1, letq=mod(i+j+O₀,2),

If there exists w and D_(0,w+q) ^(v,i,j)=1, where wε{1,2,3,4}, andVD^(v,i,j)=5, then,${B_{0}^{v,i,j} = {{int}\left( \frac{{mod}\left( {w,4} \right)}{2} \right)}},{B_{1}^{v,i,j} = {{int}\left( \frac{w - 1}{2} \right)}},$

else,

-   -   B₀ ^(v,i,j)=B_(l) ^(v,i,j)=null.

The bits extracted are B₁ ^(h,i,j) B₀ ^(h,i,j), i.e. if the 1^(st)position on the edge is a black dot, the bits are 00; if the 2^(nd)position on the edge is a black dot, the bits are 01; if the 3^(rd)position on the edge is a black dot, the bits are 11; if the 4^(th)position on the edge is a black dot, the bits are 10. Note that 00, 01,11, 10 is a Gray code, which ensures that the number of error bits is atmost 1 if the position of black dot is incorrect. See FIG. 20, whichassumes H″, V″ is the same as H′, V′ for an illustration.

Recall that a total of 8 bits are encoded in an EIC symbol. Each bit isa bit from an m-array (one dimension). Bits are now obtained from eachdimension.

Let B_(b) ^(m,n) be the bit of dimension b, where b=0, 1, . . . , 7,encoded in EIC symbol (m, n), where (m, n) are the coordinates of thesymbol in X′, Y′ coordinate system. Let C_(b) ^(m,n) be the confidenceof bit B_(b) ^(m,n) (FIG. 32).

Note that B_(b) ^(m,n) is a matrix in which substantially all the bitsencoded in all the EIC symbols in the section of EIC symbol arrayencompassing the image, are stored. Each element (m, n) in matrix B_(b)^(m,n) corresponds to a square (formed by the horizontal and verticaldashed lines in FIG. 32) whose top-left corner has the coordinates of(m, n) in X′, Y′ coordinate system.

For EIC symbols not captured in image, values of the correspondingelements in B_(b) ^(m,n) will be null. Even if EIC symbols are capturedin image, if we are unable to extract the bits encoded in the symbols,values of the corresponding elements in B_(b) ^(m,n) will also be null.Only when bits are extracted, the corresponding elements in B_(b) ^(m,n)will have the value of the bits.

We now store all the extracted bits in B_(b) ^(m,n), and theirconfidence values in C_(b) ^(m,n).

For each dimension b, where b=0, 1, . . . , 7, initialize B_(b) ^(m,n)and C_(b) ^(m,n) as:

-   -   B_(b) ^(m,n)=null,    -   C_(b) ^(m,n)=null.

For each bit l on edge (i, j) on H line, where i=0,1, . . . ,N_(h) ⁰−1,j=0,1, . . . N_(v) ⁰, l=0, 1, find the corresponding b, m and n, andassign values to B_(b) ^(m,n) and C_(b) ^(m,n):${b = {2 + l + {2 \cdot {{mod}\left( {{i + j + O_{0}},2} \right)}}}},{m = {{int}\left( {{{int}\left( \frac{N_{v}^{0} + O_{0}}{2} \right)} + \frac{i - j + O_{0}}{2}} \right)}},{n = {{int}\left( \frac{i + j + O_{0}}{2} \right)}},{B_{b}^{m,n} = B_{l}^{h,i,j}},{C_{b}^{m,n} = {{Diff}_{0}^{h,i,j}.}}$

For each bit l on edge (i, j) on V line, where i=0,1, . . . , N_(h) ⁰,j=0,1, . . . , N_(v) ⁰−1, l=0, 1, find the corresponding b, m and n, andassign values to B_(b) ^(m,n) and C_(b) ^(m,n):${b = {l + {6 \cdot {{mod}\left( {{i + j + O_{0}},2} \right)}}}},{m = {{{int}\left( {{{int}\left( \frac{N_{v}^{0} + O_{0}}{2} \right)} + \frac{i - j + O_{0}}{2}} \right)} - {{mod}\left( {{i + j + O_{0}},2} \right)}}},{n = {{int}\left( \frac{i + j + O_{0}}{2} \right)}},{B_{b}^{m,n} = B_{l}^{v,i,j}},{C_{b}^{m,n} = {{Diff}_{0}^{v,i,j}.}}$

We now normalize the confidence values. Let C_(max)=max(C_(b) ^(m,n)),where B_(b) ^(m,n)≠null. The normalized confidence values are:$C_{b}^{m,n} = {{{int}\left( {100 \cdot \frac{C_{b}^{m,n}}{C_{\max}}} \right)}.}$

This completes EIC symbol recognition in accordance with embodiments ofthe invention. Output of EIC symbol recognition is homography matrixH_(Symbol→Image), which is shown as homography matrix 1624 in FIG. 16,matrix B_(b) ^(m,n) containing the extracted bits, and matrix C_(b)^(m,n) containing the confidence values of the bits. Matrix B_(b) ^(m,n)and matrix C_(b) ^(m,n) are shown as EIC bits 1620 in FIG. 16.

As can be appreciated by one skilled in the art, a computer system withan associated computer-readable medium containing instructions forcontrolling the computer system can be utilized to implement theexemplary embodiments that are disclosed herein. The computer system mayinclude at least one computer such as a microprocessor, digital signalprocessor, and associated peripheral electronic circuitry.

Although the invention has been defined using the appended claims, theseclaims are illustrative in that the invention is intended to include theelements and steps described herein in any combination or subcombination. Accordingly, there are any number of alternativecombinations for defining the invention, which incorporate one or moreelements from the specification, including the description, claims, anddrawings, in various combinations or sub combinations. It will beapparent to those skilled in the relevant technology, in light of thepresent specification, that alternate combinations of aspects of theinvention, either alone or in combination with one or more elements orsteps defined herein, may be utilized as modifications or alterations ofthe invention or as part of the invention. It is intended that thewritten description of the invention contained herein covers all suchmodifications and alterations.

1. A system that recognizes embedded interaction code (EIC) symbols, thesystem comprising: an EIC-dot-detection module that takes effective EICsymbols, which have been generated by processing an image containing theEIC symbols, as input and produces EIC dots as output by obtaininggraylevels of selected positions of the EIC symbols; anEIC-symbol-orientation-determination module that takes the EIC dots asinput and produces rotated EIC dots as output by determining which gridcells correspond to the EIC symbols and by determining which directionis a correct orientation of the EIC symbols; and an EIC-bit-extractionmodule that takes the rotated EIC dots as input and produces EIC bits asoutput based on graylevels of selected positions of the rotated EICdots.
 2. The system of claim 1, wherein the EIC-dot-detection moduledetects black dots from the obtained graylevels of selected positions ofthe EIC symbols.
 3. The system of claim 2, wherein theEIC-bit-extraction module extracts EIC bits from the rotated EIC dotsbased on positions of black dots in the rotated EIC dots.
 4. The systemof claim 3, wherein the EIC-bit-extraction module extracts EIC bitsbased on whether a predetermined number of neighboring dots of a blackdot in the rotated EIC dots are valid.
 5. The system of claim 1, whereinthe EIC-symbol-orientation-determination module generates an updatedhomography matrix with orientation information that transforms acoordinate system of a section of an EIC symbol array encompassing theimage to a coordinate system of the image.
 6. The system of claim 1,wherein the EIC-bit-extraction module produces as output respectiveconfidence values that correspond to the EIC bits.
 7. The system ofclaim 1, wherein the EIC-symbol-orientation-determination moduledetermines which grid cells correspond to the EIC symbols and whichdirection is a correct orientation of the EIC symbols by determining howmany black dots appear at orientation-dot positions in the EIC dots. 8.A computer-readable medium containing computer-executable instructionsfor recognizing embedded interaction code (EIC) symbols by performingsteps comprising: generating EIC dots based on effective EIC symbols,which have been generated by processing an image containing the EICsymbols, by obtaining graylevels of selected positions of theEIC-symbols; generating rotated EIC dots based on the EIC dots bydetermining which grid cells correspond to the EIC symbols and bydetermining which direction is a correct orientation of the EIC symbols;updating a homography matrix with orientation information based on theEIC dots; and extracting EIC bits from the rotated EIC dots based ongraylevels of selected positions of the rotated EIC dots.
 9. Thecomputer-readable medium of claim 8, containing furthercomputer-executable instructions for detecting black dots from theobtained graylevels of selected positions of the EIC symbols.
 10. Thecomputer-readable medium of claim 9, containing furthercomputer-executable instructions for extracting EIC bits from therotated EIC dots based on positions of black dots in the rotated EICdots.
 11. The computer-readable medium of claim 8, containing furthercomputer-executable instructions for extracting EIC bits based onwhether a predetermined number of neighboring dots of a black dot in therotated EIC dots are valid.
 12. The computer-readable medium of claim 8,wherein the updated homography matrix transforms a coordinate system ofa section of an EIC symbol array encompassing the image to a coordinatesystem of the image.
 13. The computer-readable medium of claim 8,containing further computer-executable instructions for generatingrespective confidence values that correspond to the EIC bits.
 14. Thecomputer-readable medium of claim 8, containing furthercomputer-executable instructions for determining which grid cellscorrespond to the EIC symbols and which direction is a correctorientation of the EIC symbols by determining how many black dots appearat orientation-dot positions in the EIC dots.
 15. A system forrecognizing embedded interaction code (EIC) symbols, the systemcomprising: means for generating EIC dots based on effective EICsymbols, which have been generated by processing an image containing theEIC symbols, by obtaining graylevels of selected positions of theEIC-symbols; means for generating rotated EIC dots by determining whichgrid cells correspond to the EIC symbols and by determining whichdirection is a correct orientation of the EIC symbols; means forupdating a homography matrix with orientation information based on theEIC dots; and means for extracting EIC bits from the rotated EIC dotsbased on graylevels of selected positions of the rotated EIC dots. 16.The system of claim 15, further comprising means for detecting blackdots from the obtained graylevels of selected positions of the EICsymbols.
 17. The system of claim 15, further comprising means forextracting EIC bits from the rotated EIC dots based on positions ofblack dots in the rotated EIC dots.
 18. The system of claim 15, furthercomprising means for extracting EIC bits based on whether apredetermined number of neighboring dots of a black dot in the rotatedEIC dots are valid.
 19. The system of claim 15, further comprising meansfor generating respective confidence values that correspond to the EICbits.
 20. The system of claim 15, further comprising means fordetermining which grid cells correspond to the EIC symbols and whichdirection is a correct orientation of the EIC symbols by determining howmany black dots appear at orientation-dot positions in the EIC dots.